Geodesics on Riemann Surfaces and their corresponding Limit Points
Journal article, 2003

The motivation of this paper is twofold. We address the following question, left open by the author in an earlier paper \cite{asf} dealing with a connection of discrete groups and potential theory. Let $\n$ be the set on the unit sphere where a union of hyperbolic spheres centered at each orbitpoint of a discrete group is not minimally thin.{\em Is $\n$ equal to the conical limit set?} We will show that this is not true in general by constructing a counterexample in Section \ref{sec.jg}. The construction utilizes results derived while considering a problem, suggested to the author by Chris Bishop, about generalizing the well known result which gives the correspondence between returning geodesics on Riemann manifolds and conical limit points.

Kleinian group

horocycle

non-tangential limit set

minimal thinness

limit set

Fuchsian group

Discrete group

Author

Torbjörn Lundh

Chalmers, Department of Mathematics

University of Gothenburg

Michigan Mathematical Journal

0026-2285 (ISSN)

Vol. 51 279-304

Subject Categories

Mathematical Analysis

More information

Created

10/7/2017